The two-time Wimbledon champion, who underwent a procedure to resurface his hip joint earlier this year, came through 7-6(6) 6-7(4) 6-1 in Beijing in a match which lasted eight minutes short of three hours to demonstrate his continuing return to form.
Murray, who showed flashes of the touch which took him to the top of the world rankings, had to battle his way through fatigue a day after beating US Open semi-finalist Matteo Berrettini.
The 32-year-old put himself in the driving seat in a tight first set, which he took on an equally hard-fought tie-break, but the drama did not stop there.
Norrie hit back as his compatriot tired, breaking in the sixth game of the second to lead 4-2 before holding to extend his advantage.
However, Murray reeled off three games in a row, surviving a set point in the process, on the way to securing a second tie-break.
But Norrie raced into a 3-0 lead and Murray never quite got himself back into it to go down 7-4.
The double Olympic champion found new reserves at the start of the third set, holding to love in each of his fist two service games either side of an early break, and he never looked back.
Murray broke for the second time in the set to leave himself within two games of victory and although Norrie finally broke his duck to make it 5-1, that only delayed the inevitable.